Use powers of 2 to perform each calculation without a calculator or other technology(2^7⋅2^5)/16

Answer:[tex]\frac{2^{7} . 2^{5} }{16}[/tex] = 256Step-by-step explanation:The given expression is [tex]\frac{2^{7} . 2^{5} }{16}[/tex]Now, the Laws of Exponents state that 1. [tex]a^{x}.a^{y}   = a^{(x+ y)}[/tex]2. [tex]\frac{a^{x} }{a^{y} }  = a^{(x-y)}[/tex]Now, simplifying the expression using the two laws, we get[tex]\frac{2^{7} . 2^{5} }{16}[/tex]  = [tex]\frac{2^{7 + 5}  }{16}[/tex]Now,  [tex]16 = 2^{4}[/tex]So, substituting 16 with it, we get [tex]\frac{2^{7 + 5}  }{16}[/tex] = [tex]\frac{2^{12}  }{2^{4}}[/tex]= [tex]2^{12 - 4}  = 2^{8}[/tex]Simplyimng this further, we get [tex]2^{8} = 256[/tex]⇒ [tex]\frac{2^{7} . 2^{5} }{16}[/tex] = 256